In modem computed tomography (CT) scanner systems, an X-ray source generates an X-ray beam which interrogates an object and is incident on a sensor array. In third-generation CT systems, the source and sensor array are mounted on a gantry which rotates about the object. Successive sets of projections of the object are recorded at incremental gantry rotation angles. After completion of a half rotation of the gantry ("half-scan" system) or a full rotation ("full-scan" system), data from the successive rotation angles are combined in a process known as reconstruction to create a cross-sectional image of the object. In a stationary scan configuration, the object is fixed in position during each scan, while in a translational scan, or "helical" scan, the object and gantry translate relative to one another during a rotational scan, improving system throughput.
In a conventional two-dimensional CT scanner, as shown in Prior Art FIG. 1, the X-ray beam 51 propagates in a planar fan shape 50 between a point source 54 and a sensor array 52 comprising a one-dimensional array of detector elements 53. The fan beam 50 is referred to as a "transaxial fan" because the plane of the fan is perpendicular to the rotation axis, i.e., the z-axis. A two-dimensional image reconstruction process collects the raw data at each rotation angle and following a half-scan, or full-scan, converts the data into a planar pixel image of the portion of the object 55 through which the x-rays have passed. Following each scan, the object may be translated along the z-axis to generate adjacent planar cross-sectional images or "slices" of the object 55 which can be combined to produce a volumetric image.
In a three-dimensional CT scanner, as shown in Prior Art FIG. 2, a conical X-ray beam 61, also referred to as a "cone beam", generated at a point source 54, projects along beam axis y through an object 55 and is incident on a two-dimensional sensor array 63. The array 63 comprises multiple rows 56 (rows 1 . . . M) and multiple columns 62 (columns 1 . . . N of detectors which lie on a cylindrical surface 58. In this configuration, the X-ray cone beam 61 diverges not only along the xy-plane but also diverges along the z-axis.
Each cone beam 61 is composed of multiple layers of transaxial fan beams, three of which are indicated by the numerals 60A, 60B, 60C, each transaxial beam defined between the x-ray point source 54 and one of the rows 1 . . . M of detector elements 56A, 56B, 56C. Note that with the exception of transaxial fan beam 60B, which lies along the xy-plane, the remaining transaxial fan beams, such as beams 60A, 60C, are not perpendicular to the z-axis of rotation, and therefore are not "transaxial" in the strictest sense. Instead, each remaining fan beam, such as either beam 60A, 60C is tilted relative to the xy-plane by a small angle .beta., referred to as the "conical angle" as shown in Prior Art FIG. 3. Within this definition, transaxial fan beam 60B, projected along the xy-plane can be envisioned as a transaxial fan beam having a conical angle of 0.degree..
The x-ray point source 54 and respective columns 1 . . . N of detector elements 62 also define "axial" fan beams, three of which are indicated by numerals 64A, 64B, 64C as illustrated in Prior Art FIG. 4. Each axial fan beam 64 lies on a plane parallel to the rotation axis. With the exception of the fan beam 64B of detector column j.sub.o, which lies directly on the yz-plane and therefore projects through the z-axis at all rotation angles, the axial fans of the remaining columns 1 . . . N diverge from the yz-plane by an "axial angle" of .gamma.. The central axial fan beam 64B, projected along the yz-plane can be envisioned as an axial fan beam having an axial angle .gamma. of 0.degree.. While in rotation, a set of line projections are provided at each of a plurality of successive rotation angles of the gantry. The angle of a line projection measured on the xy-plane is referred to as the view angle of the projection. Thus, at rotation angle .theta., the line projection within each axial fan beam at axial angle .gamma. is associated with the same view angle of .phi.=.theta.+.gamma..
In practice, a conventional two-dimensional reconstruction algorithm is insufficient for reconstructing a three-dimensional volumetric image from cone-beam data collected with a two-dimensional detector array. The three-dimensional cone-beam data cannot be accurately resolved into independent parallel layers along the z-axis for introduction into two-dimensional reconstruction since each transaxial fan beam lies at a conical angle .beta. to the z-axis, as described above. Performing two-dimensional reconstruction using this data would therefore result in reconstruction errors for each set of fan beam data, with the exception of the central fan beam 60B along the xy-plane. The reconstruction errors worsen as the conical angle .beta. increases. A more accurate three-dimensional reconstruction technique known as cone-beam reconstruction for stationary scan configurations is described in:
1. L. A. Feldkamp, L. C. Davis, and J. W. Kress, "Practical Cone-beam Algorithm", J. Opt. Soc. Am. A, Vol.1, p612, No.6, June 1984. PA1 2. U.S. Pat. No. 5,291,402 issued Mar. 1, 1994, to A. H. Pfoh, "Helical Scanning Computed Tomography Apparatus"; PA1 3. U.S. Pat. No. 5,377,250 issued Dec. 27, 1994, to H. Hu,"Reconstruction Method for Helical Scanning Computed Tomography Apparatus with Multi-row Detector Array"; PA1 4. U.S. Pat. No. 5,430,783 issued Jul. 4, 1995, to H. Hu, N. J. Pele, and A. H. Pfoh, "Reconstruction Method for Helical Scanning Computed Tomography Apparatus with Multi-row Detector Array Employing Overlapping Beams"; and PA1 5. D. L. Parker, "Optimal Short Scan Convolution Reconstruction for Fan beam CT", Med. Phys., Vol.9, No.2, p254, March/April 1982.
The foregoing discussion applies to scanning an object which is stationary with respect to the z-axis. In another form of scanning, known in the art as a helical scan, the object and gantry translate relative to one another along a translation axis (typically, the object is translated relative to the gantry), usually parallel to the z-axis, at a constant speed during gantry rotation. From the perspective of the object, the x-ray source and sensors can be envisioned as circling about the object in a helical trajectory during data collection. In a helical scan of a conventional system with single-row detectors, the projection data are first interpolated to the z position of each slice for generating its planar image. These planar images are located contiguously along the z-axis. The contiguous slices can be combined and further processed for various modes of three-dimensional display. Unfortunately, in a cone-beam system, the z-axis translation causes the collected data to deviate further from that data which is required for standard two-dimensional or three-dimensional reconstruction techniques. As a result, the reconstruction errors arising from a helical scan of a cone-beam system are worse than that of a stationary scan. Reconstruction and enhancement methods for cone-beam helical scans are described in:
In the foregoing references, data are collected over a full rotation of the gantry, i.e., "full-scan", to reconstruct the volumetric image over the scanned region. However, the image may be reconstructed based on data collected in half rotation of the gantry, i.e., "half-scan". Half-scan imaging offers the advantage of doubling the throughput rate or "pitch" compared to a full-scan, where "pitch" is the extent of object translation along the z-axis during a full rotation of the gantry. In a stationary cone-beam system, the full-scan reconstruction technique provides images generally superior to those of the half-scan reconstruction technique. This is due to the fact that in a full scan, the axial fan beams 66, 68 at view angles .phi. and .phi.+.pi. respectively diverge in opposite directions as sketched in Prior Art FIG. 5A, which, when the data is reordered with data from other mutually-opposing views, tends to cancel some of the reconstruction errors. On the other hand, at each view angle .phi. of a half scan, there is no corresponding fan beam 68 at view angle .phi.+.pi. which presents an opposite view of the same region of the object.
In a helical scan as shown in Prior Art FIG. 5B, the opposing axial fan beams 66, 68 at view angles .phi. and .phi.+.pi. respectively do not correspond to the same z position. As a result, a helical full-scan contains larger reconstruction errors than a stationary full scan. In both full-scan and half-scan cone-beam systems, reconstruction errors increase with increased divergence of the axial X-ray beam. If additional detector rows 56 are used, or if the width of each row increases, reconstruction errors become more severe as the result of increasing the conical angle .beta..